For what values of \$d\$ can you reduce \$d\$-coloring polynomially to \$d + 1\$ coloring?

For what values of $$d$$ can you reduce $$d$$-coloring polynomially to $$d + 1$$ coloring?

This is a problem that I’ve been thinking about for a while. Assuming 3-Sat and 3-coloring are NP Complete, for what values of $$d$$ am I able to polynomially reduce $$d$$-coloring to $$d+1$$ coloring and $$d$$-coloring to $$d-1$$ coloring?

Thanks